read this and then decide if Yahoo is secure
Yahoo! webmail! hijacks! are! back!... ? The Register
its still a problem - I was dealing with one today
NO web service is secure unless you have the site encryption, user list, access passwords totally locked down. Yahoo groups is certainly not that.
If you are handling the kind of personal information you state, then GGroups almost certainly does not have the kind of security required by the Data Protection Act. Nor will any other similar service.
You need to look at your own dedicated server, with secure connections.